A000236

[Max]

I've got the second paper from A000236 references (I can share if anybody interested), i.e.,

J. R. Rabung and J. H. Jordan, Consecutive power residues or nonresidues, Math. Comp., 24 (1970), 737-740.

and implemented approach outlined there (actually, much optimized).
Then I've recomputed A000236 from scratch and got
3, 8, 20, 44, 80, 343, 351, 608, 1403
that disagree with the paper (and the current content of A000236) at a(8).

The paper claims a(8)=399 based on the following placement of the primes <399 into 8th-power classes:
Class 1: 3, 89, 107, 113, 131, 149, 163, 167, 173, 197, 227, 229, 251, 257, 269, 293, 307, 311, 317, 353
Class 2: 17, 53, 59, 71, 101, 137, 281, 389
Class 3: 83
Class 4: 2, 5, 11, 23, 41, 47
Class 5: 29
Class 7: 19
Class 0: the others

But it is easy to see that for this placement consecutive residues 80 and 81 fall into the same Class 4:
class(80) = class(2^4*5) = 4*class(2)+class(5) = 4*4+4 = 4 (mod 8)
class(81) = class(3^4) = 4*class(3) = 4*1 = 4 (mod 8)
and so do 248 and 249.

The placement of the primes<351 supporting a(8)=351 generated by my program:
Class 1: 2, 19, 53, 103, 107, 113, 127, 131, 233, 251, 257, 269, 271, 317, 337
Class 2: 11, 59, 61, 67, 109, 137, 173
Class 3: 37
Class 4: 41, 47
Class 5: 5, 13, 29
Class 6: 3, 7, 17, 31, 43
Class 7: 23
Class 0: the others

Max

Max wrote:
> David Wilson wrote:
> 
>>    (d) a(k) has the same defintiion as b(k), the paper gave correct 
>> values for a which were improperly transcribed to A000236.
> 
> Since the review lists values coinciding with A000236, (d) is not the 
> case either.
> 
> The best thing we can do is to go to a library and carefully inspect the 
> original paper.
> I will try to do so this week.
> 
> Max
> 
> 
> 
>